An su(1,1) dynamical algebra for the Poschl-Teller potential

摘要

An su(1, 1) dynamical algebra to describe the continuum part of the spectrum for the modified Poschl-Teller potential is proposed. The space associated with this algebra is given in terms of a family of orthonormal functions {Phi(n)(sigma)} characterized by the parameter sigma. This set is constructed from polynomials which are orthogonal with respect to a weighting function corresponding to a Poschl-Teller ground state. An analysis of the associated algebra is investigated in detail. The functions are identified with Poschl-Teller-like functions associated with different potential depths. We prove that by choosing appropriately the parameter sigma it is possible to decouple the discrete states of a given parity from the continuum part of the spectrum. A discussion of the matrix elements of the dipole function operator is also included. [References: 47]